Efficient approximations of dispersion relations in optical waveguides with varying refractive-index profiles

Yutian LI, Jianxin Zhu

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper we consider the problem of computing the eigenmodes for the varying refractive-index profile in an open waveguide. We first approximate the refractive-index by a piecewise polynomial of degree two, and the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Kummer functions. Then, analytical approximate dispersion equations are established for both TE and TM cases. Furthermore, the approximate dispersion equations converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Suitable numerical methods, such as Müller's method or the chord secant method, may be applied to the dispersion relations to compute the eigenmodes. Numerical simulations show that our method is very practical and efficient for computing eigenmodes.

Original languageEnglish
Pages (from-to)11952-11964
Number of pages13
JournalOptics Express
Volume23
Issue number9
DOIs
Publication statusPublished - 4 May 2015

Scopus Subject Areas

  • Atomic and Molecular Physics, and Optics

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